Protesters add notes to a damaged car after four days of demonstrations against the Turkish government in Istanbul. Photograph: Tolga Bozoglu/EPA

Sitting on the grass in Taksim Square's Gezi Park, university English tutor Serem Ramau helps some of her students with their homework. Less than 24 hours after some of the biggest demonstrations against the Turkish government in years, the park has been transformed, at least for the time being. The only evidence of the weekend turmoil are the banners and posters on the fences, walls and trees.

Ramau explains why she and her pupils joined the protests. "The people just want to be able to express themselves, but [Turkish Prime Minister Recep Tayyip] Erdogan wants an authoritarian regime. We reject that, and that is why we are here."

Resting in the shade of a tree next to a stand manned by the LGBT activists of Lambda Istanbul, 29-year-old consultant Onur Aygünes said that for the first time he felt as if there was real momentum behind a larger political movement: "My friends and I felt increasingly oppressed in Turkey, but this is very inspiring. Most of the people here have never been politically active."

Aygünes, who has participated in rallies such as the Istanbul Gay Pride or Mayday demonstrations, believes the excessive police violence used in the square was counter-productive, bringing more and more people onto the streets, rather than deterring them. "I have been teargassed for the first time here, and all it did was to make me more determined."

A large group of students pay tribute to modern Turkey's founder, chanting "We are Mustafa Kemal's soldiers" as they walk past a handwritten sign, which reads "We will not kill, we will not be killed, we are not anyone's soldiers" – the slogan of the anti-militarist movement in Turkey. Flags of the environmentalist movement, rainbow banners, flags of Atatürk, of Che Guevara, of different trade unions, all adorn the park. Trees bear the names of the recent car bomb attack victims in Reyhanli, and of the 35 civilians killed in a Turkish airstrike on the Iraqi border in 2011.

"We are neither anti-Islamist nor anti-secularist," Aygünes says. "All groups of society are here, this is the first time this happens, I am so excited!"

While Istanbul's urban middle class largely fuels the protest movement, others in Gezi Park are also disaffected. Manning a watermelon cart, Kurdish fruit seller Hüseyin Avci airs his grievances: "The zabita [municipal police] barely leave any room for me to make any money anymore. The cart is my only source of income. The AKP cracks down on mobile street sellers, but does not offer any alternatives," he said, referring to the governing Justice and Development party of the prime minister.

Alihan Kirac, 27, voiced similar gripes: "My whole family is in retail. Erdogan wants to build shopping malls everywhere, even in the city centre. How are we supposed to make any money?"

Like many protesters, Kirac strongly objects to Erdogan's perceived high-handedness. "He doesn't listen to anyone. He gets richer every day, and he doesn't care about us." Having supported the AKP in the past, he added: "I certainly will not vote for them again."

A few volunteers hand out food, water, clothing, umbrellas and medical supplies at a table erected by activists; a handwritten sign asks for donations of blankets, tents, raingear.

"People donate all of these things," says 20-year-old economics student Doruk Keskin. "And we hand them out for free to anyone who asks."

Keskin is not sure how many volunteers work at the supply station: "We organise everything ourselves and it works very well. This is not just the Gezi Park movement anymore; this is a movement of the people."

As if to prove his point, a woman in her 50s arrived with a plastic bag full of fresh bread while at a neighbouring stand, an elderly man asks for tea.

Just a few metres down the path, a group of women in smart office clothes gath, carrying flags bearing the portrait of Atatürk, the revered founder of the republic. "We will not go to work today," one of them says, laughing. "Our boss supports this protest."

"We are here because we are fed up with this government that tries to limit our freedom. Enough is enough", said Ebru Yilmaz, 37. "We are the children of Mustafa Kemal Atatürk, the greatest leader of all times!"

However, some protesters worry about the increasingly nationalist tone of the demonstrations which started as a peaceful sit-in against the redevelopment of a small park into a kitschy Ottoman-style mall and hotel complex.

"For some people here it is completely natural to wave Turkish flags and to invoke Atatürk in their slogans," says documentary film maker Bingöl Elmas. "But for me, as a Kurd, these symbols are connected to problems that we have not solved yet in Turkey. Some people shout: 'How happy is the one who says 'I am a Turk', but that excludes us.

Aygünes regrets the absence of the pro-Kurdish Peace and Democracy party (BDP) at the protests: "I have always supported them, and I guess it's a political decision for them to remain on the sidelines for now."

The co-chair of the BDP, Selahattin Demirtas, said on Saturday that his party supported the protests against repressive government policies, but warned nationalist groups not to try and sabotage the ongoing peace talks between the Kurdistan Workers' party (PKK) and the Turkish government: "We will not allow the events in Gezi Park to turn against the peace process … Our party base does not participate in demonstrations of racists and fascists."

"The clearest split between nationalist west-coast Kemalists and liberal leftists runs along their attitudes towards the Kurdish issue", Onur Aygünes says. "And so far, there has not been much dialogue on the issue."

He thinks that this may change with time. "The first step is to chant protest slogans together, and the second step will be to start talking."